Question

If the ratio of radius of two cylinder of two equal hight is 1:3 find the ratio of there curved surface area​

Answer 1

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Answer 2

Given :

The ratio of radius of two cylinder of same height is 1:3.

To Find :

The ratio of their curved surface area.

Solution :

Analysis :

We have to use the curved surface area of cylinder. Here by substituting the values we can find the ratio of the curved surface areas.

Required Formula :

Curved surface area for first cylinder :

$\boxed{\bf A_1=2\pi r_1h_1}$

where,

• A₁ = Area of first cylinder
• π = 22/7
• r₁ = radius of first cylinder
• h₁ = height of first cylinder

Curved surface area for second cylinder :

$\boxed{\bf A_2=2\pi r_2h_2}$

where,

• A₂ = Area of second cylinder
• π = 22/7
• r₂ = radius of second cylinder
• h₂ = height of second cylinder

Explanation :

It is said that the height for the two cylinder is same.

So,

☯ According to the question,

$\\ :\implies\sf\dfrac{A_1}{A_2}=\dfrac{2\pi r_1h_1}{2\pi r_2h_2}$

where,

• r₁ = 1
• r₂ = 3
• h₁ = h
• h₂ = h
• π = 22/7

Using the required formula and substituting the required values,

$\\ :\implies\sf\dfrac{A_1}{A_2}=\dfrac{2\pi 1h}{2\pi 3h}$

$\\ :\implies\sf\dfrac{A_1}{A_2}=\dfrac{2\not{\pi }1\not{h}}{2\not{\pi} 3\not{h}}$

$\\ :\implies\sf\dfrac{A_1}{A_2}=\dfrac{2\times1}{2\times3}$

$\\ :\implies\sf\dfrac{A_1}{A_2}=\dfrac{2}{6}$

$\\ :\implies\sf\dfrac{A_1}{A_2}=\cancel{\dfrac{2}{6}}$

$\\ :\implies\sf\dfrac{A_1}{A_2}=\dfrac{1}{3}$

$\\ \therefore\boxed{\bf A_1:A_2=1:3.}$

The ratio of their curved surface area is 1 : 3.